Soft X-ray microscopy with diffractive optics
E. Pereiro
Outline
• Brief description of a synchrotron
• X-rays, what for?
• Soft X-ray microscopy with diffractive optics
• Two common microscopes (TXM & STXM)
• Challenges: radiation damage, depth of focus limitation
• 2 applications with TXM and STXM
Light for Science
A synchrotron is a piece of equipment that produces
synchrotron light.
electron
V : close to
c = 300 000 km/s
Synchrotron radiation
Synchrotron radiation is a set of electromagnetic waves emitted by charged particles that move within a curved
trajectory at velocities close to the speed of light.
When electrons are deflected through a magnetic field they emit synchrotron light.
An electric field accelerates an electron and increases its speed.
LINAC
Booster
RF Cavities
Synchroton Light:
IR, VL, UV, X-ray etc.
e-e-
How does it work ?
Bending Magnets
Experimental Stations
Origin of electrons
v= 60% of c
Linac
Booster
Storage Ring
Beamlines
from v = 99.998% to 99.999998% of c
v = 99.998% of c
• Optical Hutch
• Experimental Hutch
• Control Hutch
Anatomy of a Synchrotron
LINAC
The Linac is the first of the accelerators that accelerates the e- up to 100 MeV
v from 60% to 99.998% of c
Booster
Storage Ring
Accelerates the e- from 100 MeV to 3 GeV
Booster and Storage Ring
A SYNCHROTRON IS A TOOL THAT IS USED TO
STUDY THE STRUCTURE OF MATTER
Atomic
Molecular
Nano-, Micro-, Milli-metric
Science with synchrotron light
Chemistry
Physics
Biology
Materials science
Geology
Cultural Heritage
Environment
Industry
Medicine
…
APPLICATIONS
See small features in “thick” samples (3D)
Element and chemical sensitivity
Why imaging with X-rays?
Advantages of X rays compared to electrons
• thick samples
• water window: natural contrast of wet samples
• tomography in statistical numbers
• spectroscopic imaging
XRM complementary to TEM and
light microscopy
✬ radiation damage of both electrons & X-rays
A beamline
WB
diag.
Vertical focusing
mirror
Horizontal focusing
mirror
Vertical
slits
Diag.
Entrance
slit
VLS PGM
Vertical refocusing
mirror
Diag.
Exit
slit
Cryo Transmission X-ray Microscope
BM
source
30m
MISTRAL Beamline @ ALBA
Soft X-ray microscopy
with diffractive optics
Ref: Soft X-rays and Extreme Ultraviolet Radiation. Principles and Applications.
David Attwood
Soft X-ray microscopy
What for?
• imaging the internal structure of a sample.
• spectroscopic imaging to map chemical states.
How to form an image with SXR wavelengths (0.3-5 nm)?
• Refraction, as in optical microscopy (n=1.2-1.5), is impractical as n=1-δ+iβ is too close to unity (refraction is too
weak).
• Glancing incidence total external reflection with curved optics works but the image resolution is significantly
compromised by aberrations.
• Diffraction allows forming images at high resolution - tens of nm.
Transmission signal through a sample
• absorption contrast
• phase contrast
Contrast mechanism: absorption
Basic absorption and emission processes
The total cross section describes the likelihood of interaction between particles
(absorption and scattering).
dz
I0 I
photoionization fluorescent emission Auger process
ρ: mass density
µ: absorption coefficient
na: atomic density
sabsT σσσ +=
)exp()exp( 00 znIzII absaσρµ −=−= ),( ZEµµ =
Fresnel Zone Plate lensSoft X-ray microscopy uses diffractive lenses.
Courtesy of Joan Vilà
Diffraction & Scattering
DEFINITIONS
Scattering is a process by which incident radiation is redirected over a very wide angular range, generally by disordered systems
or rough surfaces.
Diffraction is the process by which radiation is redirected into well-defined directions by ordered arrays of scatterers. As the
radiation propagates away, it interferes with nearby undiffracted radiation, producing dark and bright bands known as interference
patterns.
Example: diffraction of X-rays by a crystal
Transmission grating
For small structures, diffracted radiation propagates at angles θ∼λ/d.
With repetitive structures, positive interference in certain directions can lead to a very strong redirection of E.
50% absorbed
transmission function:
1
d/4
f(ξ)
d/2 d ξ
Constructive interference occurs at angles where the path length is increased by one λ or m λ.
The fraction of incident E diffracted into the various orders depends on the nature of the periodic structure.
m=1
0
2
0
)2/sin(
)/2cos()(
IcII
m
mc
dmcf
mmm
m
m
ηππ
ξπξ
==
=
= ∑∞
∞−
The radial zones are located such that the increased path lengths through sequential transparent zones differ by one λ each and thus
add in phase at the image point.
the radius of the nth zone is given by:
A real first focus is achieved when
successive zones increase in radius by
FZP are highly chromatic
1) FZP can focus radiation
For f >> nλ/2, which corresponds to a small NA lens
Fresnel Zone Plates
Consider a circular transmission grating with the zonal periods adjusted so that at increasing radius from the optics axis the periods become
shorter, thus θ becomes larger allowing for a real focus.
fnrn λ≈
12sin <<∆== rNA λθ
n
Fresnel Zone Plates
Relationships for f and D in terms of λ, Δr and N
Important relationship for the design of FZP showing that f scales directly with N, with the square of the outer zone width (which sets the
resolution) and inversely to λ, introducing a strong chromatic effect.
2) FZP can form a real image
Successive zones, alternately transmissive and opaque, are constructed so as to add λ/2 to successive path lengths, so that
where for NA small,
(1)
(2) (3)
Combining (1), (2) and (3) with f=rn2:
and
Fresnel Zone Plates
2λnpqpq nn ++=+
qrqrqq n
nn 2
222 +≈+=p
rprpp nnn 2
222 +≈+=
fpq
111 ≈+q
pM =
FZP generates many diffractive orders (m).
Only a fraction of light goes to the 1st order.
For higher orders, mnλ/2 is added to the path
length and
3) FZP: higher diffractive orders
Fresnel Zone Plates
mn fmnr λ≈2
mffm =
In theory…
50% of the incident energy is absorbed by the opaque zones.
25% is transmitted in the forward direction: m = 0.
10% is focus onto m = 1 and 10% onto m = -1.
<5% is focus onto higher orders.
4) FZP efficiency
ηm =
1/4 m=0
1/m2π2 m odd
0 m even
…but opaque zones are difficult to manufacture and
therefore ηm depends on the material thickness and
n=1-δ-iβ.
the extra phase change introduced by the material
reinforces ηm when material and zone thickness are
conveniently chosen.
Joan Vilà, thesis
Fresnel Zone Plates
Fresnel Zone Plates
5) FZP diffraction
The FZP forms an Airy pattern in the focal plane with
characteristic lateral dimension.
The resolution of an ideal lens is limited by NA and λ.
The Airy pattern carries 85% of the power in the first ring.
Intensity distribution for a coherently illuminated FZP.
λπ /2=k
6) Spatial resolution: resolving 2 point sources
One measure of the resolution of a lens is the minimum discernible separation of 2 mutually incoherent point sources. This depends
on the point spread function, that is the image plane intensity distribution due to a distant point source. For an ideal lens, including
FZP, the PSF is an Airy pattern whose lateral extent (spread) depends on both λ and NA.
Fresnel Zone Plates
= 1.22 ∆r
for σ=0
Au Siemens star with 30 nm smallest features.
40 nm ZP at E=520 eV, t=1s.25 nm ZP at E=776 eV, t=4s
Fresnel Zone Plates
6) Spatial resolution: resolving 2 point sources
DoF = sample thickness that can be imaged allowing for only a 20% on-axis intensity decrease
7) FZP depth of focus and spectral bandwidth
Fresnel Zone Plates
FZP are highly chromatic: for precise imaging spectral bandwidth illumination should be restricted
Fresnel Zone Plates
DoF scales as λ/NA2
Optical Transfer properties with partially coherent illumination
Depending on the coherence of the illumination you can have better resolution than the Rayleigh one (1.22Δr).
Nanofabrication of Fresnel Zone Plates
e-beam lithography is used to manufacture FZP.
δz
NA = λ /2∆r = 0.03
Fresnel Zone Plates: summary
for coherent illumination!
= 2.516 mm = ± 1.342 µm for m=1
= 48.8 nm for m=1
m
rNcoherentyx
∆= 22.1,δ
λδ
2
2)(2
m
rNz
∆±=
State of the art
“Cr/Si multilayers with 15.1 nm half-period imaged with 15 nm ZP”
- efficiency ∼3%
- focal length at C edge: 100 µm
✬ low efficient (high aspect ratio)
✬ sensitive to heat load
✬ few suppliers
by Chao et al. Nature 435 (2005)
ð increasing spatial resolution implies decreasing DOF (λ/NA2)
ð higher resolution with reasonable DOF @ multi-keV
Fresnel Zone Plates
To sum up!
Two common soft X-ray microscopes
The microscopes
The scanning X-ray microscope (STXM)
1. least radiation dose
2. high spatial resolution (∆rN)
3. requires spatially coherent radiation
4. longer exposure time
5. spectroscopic capabilities
6. allows detecting fluorescent emission
1. high spatial resolution (∆rN)
2. short exposure time (snapshot)
3. higher radiation dose
4. fast 3D imaging
The transmission X-ray microscope (TXM)
The microscopes
Illumination can be provided by a FZP or a glass capillary.
A chronology of cryo Transmission X-ray Microscopy
1. X-ray projection of frozen hydrated alga
G. Schneider, Ultramicroscopy 75 (1998)
2. 1st cryo-tomo of a frozen alga
D. Weiss et al. Ultramicr. 84 (2000)
4. cryo-tomography of a yeast
C. A. Larabell et al., Mol. Bio. Cell, 15 (2005)
3. Drosophila melanogaster cell
G. Schneider et al. Surf. Rev. Lett 9, 1 (2002)
XRM focused issue (2012)
x-ray microscope
X-ray-source
HZB-BESSY II U41-XM
Berlin (Germany)
ALBA-MISTRAL
Barcelona (Spain)
CCD
OZP
sample
capillary condenser
central stop
National Center for X-ray Tomography – XM2 – ALS (Berkeley, USA)
The cryo-Transmission Soft X-ray Microscopes
Challenges: radiation damage
Radiation damage
radiation damage studies using XANES spectroscopy in PMMA
by T. Breez & C. Jacobsen, J. Synchr. Rad. 10 (2002)
with cryo no mass loss up to 1010 Gy @ 50 nm
critical dose for bond breaking ∼ 15×106 Gy
298 K
dose ∼13×106 Gy
113 K
dose ∼1010 Gy
298 K
warming up
O 1s(C=O) → πC=O*
Dose and ultimate resolution
DOSE SCALES AS THE INVERSE FOURTH POWER OF THE RESOLUTION
radiation damage sets the ultimate resolution
Calculation of dose & flux required for 3D imaging with a given resolution
• Calculation based on dose fractionation theorem (Hegerl and Hoppe (1976))
• The coherent scattering cross section of a cubic voxel is re2
λ2 |ρ|2d4.
• Therefore the dose D and the flux F required to deliver P scattered x-rays into a detector with collection angle chosen for
resolution d is
µ = the voxel intensity absorption coefficient
hν = the photon energy
re = the classical electron radius
λ = the photon wave length
ρ = the voxel electron density
ε = the density
D =µ P hν
ε
1
re2 λ2 ρ 2
d4 F=
P
re2 λ2 ρ 2
d4
Dose-resolution relationship for 3D imaging of frozen-hydrated samples
Required imaging dose (Rose criterion)
from Howells et al., JESRP (2005)
Challenges. Depth of focus limitation: what can
be done?
Depth of field limitation in soft X-ray tomography
zizo
F
F’
ff’
z
zizo
F
F’
ff’
z
zB
zA
PSF
Beer-Lambert absorption coeff.
J. Oton et al. , Image formation in cellular X-ray microscopy, J. Struct. Biol. 178 (2012)
1) missing wedge (as in ET): “elongation” along Z axis
2) depth of field smaller than sample thickness: “elongation” along
Z with a strong radial component.
z-dependence blurring is worse than missing wedge (both
happen)
Blurring in soft X-ray tomography?
40 nm ZP ∼2.6 µm depth of field @ 520 eV
What can be done? We need to explore
1. dual axis tomography could be explored
2. deconvolution of the Point Spread Function (PSF) of the lens
( , ) ( , , ( , ))i ih z z h x y D z z≡
( , , )x y zµ
Applications: 3D imaging & spectroscopic imaging
Soft X-ray tomography of a cryo-fixed cell
3D X-ray tomograms of mouse adenocarcinoma cells showing
many subcellular organelles:
mitochondria (M)
lyosomes (L)
endoplasmic reticulum (ER)
vesicles (V)
plasma membrane (PM)
nuclear membrane (NM)
nuclear pores (NP)
nucleoli (Nu)
nuclear membrane channels (NMC)
a, c, d, e & f acquired with 25-nm ZP at 510 eV
b acquired with 40-nm ZP.
Pixel sizes and slice thicknesses are 9.8 nm (a, c -f) and 15.6 nm
(b).
Scale bars = 0.39 µm.
G. Schneider et al., Three-dimensional cellular structure resolved by X-ray microscopy, Nature Methods 7, 985-987 (2010)
Applications: 3D imaging
red: iron
blue: phosphorus
green: zinc
Mammalian spermatozoa
Bohic et al. J. Struct. Biology 177 (2012)
Selenium and zinc are necessary for motility and thus
are often associated with infertility.
Applications: Spectroscopic imaging
Hard X-ray 2D spectroscopic imaging
Thank you for your attention!
Computed Tomography
1D Fourier transform of a projection corresponds to a slice of the 2D Fourier transform of the original
object
Applications: Spectroscopic imaging
Elements of living cells: H, C, N and O constitute 96% by weight
Na, Mg, P, S, Cl, K and Ca make up the remaining 4%
Examples of hard X-ray STXM:
- Subcellular X-ray fluorescence imaging as a tool to understand metal-induced pathologies.
- Zinc in stem cell differentiation
L. Finney et al., XRM2010
communication (APS)